Need help with Combinatorics Problem!!!!

Let S be the set of all binary strings where every block of 1's have even length. (a) Determine an unambiguous expression for S. Explain your answer. (b) Determine the generating series of S with respect to the lengths of the strings. Simplify your answer as much as possible. (e) Let an be the number of strings in S of length n. Use part (b) to prove that for all n 2 2, an = tin1 + i1n2- (d) Give a combinatorial proof of the equation in part (c) using a bijection. For any bijection that you use, you need to (1) define the domain and codomain; (2) define the function; (3) write down the inverse; and (4) show that both the function and the inverse are welldefined. You do not need to prove that your inverse is correct, but it should be clear that it reverses the operation of f